To solve the equation \( x^2 = 81 \) by inspection, we can look for values of \( x \) that satisfy the equation.
We know that \( 81 \) is a perfect square. The square root of \( 81 \) is \( 9 \). Thus, we have:
\[ x = 9 \quad \text{or} \quad x = -9 \]
These can be derived from the fact that if \( x^2 = 81 \), then:
\[ x = \sqrt{81} \quad \text{or} \quad x = -\sqrt{81} \]
Thus, the complete solution set is:
\[ { 9, -9 } \]